UNFOLDING FINITIST ARITHMETIC

Unfolding Finitist Arithmetic

The concept of the (full) unfolding U(S) of a schematic system S is used to answer the following question: Which operations and predicates, and which principles concerning them, ought to be accepted if one has accepted S? The program to determine U(S) for various systems S of foundational significance was previously carried out for a system of non-finitist arithmetic, NFA; it was shown that U(N...

The unfolding of non-finitist arithmetic

The unfolding of schematic formal systems is a novel concept which was initiated in Feferman 6]. This paper is mainly concerned with the proof-theoretic analysis of various unfolding systems for non-nitist arithmetic NFA. In particular , we examine two restricted unfoldings U 0 (NFA) and U 1 (NFA), as well as a full unfolding, U(NFA). The principal results then state: (i) U 0 (NFA) is equivalen...

The unfolding of non- nitist arithmetic

The unfolding of schematic formal systems is a novel concept which was initiated in Feferman [6]. This paper is mainly concerned with the proof-theoretic analysis of various unfolding systems for nonnitist arithmetic NFA. In particular, we examine two restricted unfoldings U0(NFA) and U1(NFA), as well as a full unfolding, U(NFA). The principal results then state: (i) U0(NFA) is equivalent to PA...

Unfolding feasible arithmetic and weak truth

In this paper we continue Feferman’s unfolding program initiated in [11] which uses the concept of the unfolding U(S) of a schematic system S in order to describe those operations, predicates and principles concerning them, which are implicit in the acceptance of S. The program has been carried through for a schematic system of non-finitist arithmetic NFA in Feferman and Strahm [13] and for a s...

Toward finitist proof theory